6533b839fe1ef96bd12a5b5e

RESEARCH PRODUCT

X-ray Tomography of One-forms with Partial Data

Keijo MönkkönenJoonas Ilmavirta

subject

Mathematics - Differential Geometry46F12 44A12 58A10Open set01 natural sciencesinversio-ongelmatintegraaliyhtälötSet (abstract data type)vector field tomographytomografiaFOS: MathematicsNormal operator0101 mathematicsMathematicsx-ray tomographyinverse problemsEuclidean spaceApplied MathematicsMathematical analysisInverse problemunique continuationnormal operatorFunctional Analysis (math.FA)Mathematics - Functional Analysis010101 applied mathematicsComputational MathematicsDifferential Geometry (math.DG)röntgenkuvausTomographyfunktionaalianalyysiAnalysis

description

If the integrals of a one-form over all lines meeting a small open set vanish and the form is closed in this set, then the one-form is exact in the whole Euclidean space. We obtain a unique continuation result for the normal operator of the X-ray transform of one-forms, and this leads to one of our two proofs of the partial data result. Our proofs apply to compactly supported covector-valued distributions.

https://doi.org/10.1137/20m1344779